To find the measure of <FEG and <HEG, we need to use some knowledge about two intersecting lines. We know that m<DEF = 129°. That means that we can easily find the measure of angle HEG. That's because DEF and HEG are vertical angles, and by the Vertical Angles Theorem, we know that they are equal in measure. That means that m<HEG = 129°. Now onto <FEG. Since the angles DEF and FEG are on a straight line, that means that they will have measures that add up to 180° (they are supplementary). Since DEF = 129, that means that 129° + x° = 180°, meaning that x = 51°. That means that m<FEG = 51°.
